Conventionally, there has been widely known an air-fuel ratio control apparatus which controls an air-fuel ratio based on outputs of an upstream air-fuel ratio sensor and a downstream air-fuel ratio sensor, both disposed in an exhaust passage of an internal combustion engine (refer to, for example, Japanese Patent Application Laid-Open (kokai) Nos. Hei 6-317204, 2003-314334, 2004-183585, 2005-120869, and 2005-273524). The upstream air-fuel ratio sensor is disposed upstream of an exhaust gas purifying catalyst (the most upstream catalyst, if two of the catalysts are provided) for purifying an exhaust gas from cylinders, in an exhaust gas flowing direction. In contrast, the downstream air-fuel ratio sensor is disposed downstream of the exhaust gas purifying catalyst in the exhaust gas flowing direction.
As the downstream air-fuel ratio sensor, a so-called oxygen sensor (also referred to as an O2 sensor) is widely used, which has (shows) a step-like response in the vicinity of the stoichiometric air-fuel ratio (Z-response: response that the output drastically changes in a stepwise fashion between a rich-side and a lean-side with respect to the stoichiometric air-fuel ratio). As the upstream air-fuel ratio sensor, the above described oxygen sensor, or a so-called A/F sensor (also referred to as a linear O2 sensor) is widely used, whose output proportionally varies in accordance with the air-fuel ratio.
In those apparatuses, a fuel injection amount is feedback-controlled in such a manner that an air-fuel of the exhaust gas flowing into the exhaust gas purifying catalyst coincides with a target air-fuel ratio, based on an output signal from the upstream air-fuel ratio sensor (hereinafter, this control is referred to as a “main feedback control”). In addition to the main feedback control, a control to use an output signal from the downstream air-fuel ratio sensor in a feedback control for the fuel injection amount is also carried out (hereinafter, this control is referred to as a “sub feedback control”).
Specifically, in the sub feedback control, a sub feedback correction amount is calculated based on the output signal from the downstream air-fuel ratio sensor (more specifically, based on a deviation between the output signal and a target voltage corresponding to a target air-fuel ratio). The sub feedback correction amount is used in the main feedback control so that a deviation between the air-fuel ratio of the exhaust gas corresponding to the output signal from the upstream air-fuel ratio sensor and the target air-fuel ratio is compensated.
In the mean time, as the exhaust gas purifying catalyst, a so-called three-way catalyst is widely used, which can simultaneously purify unburnt substance, such as carbon monoxide (CO) and hydrocarbon (HC), and nitrogen oxide (NOx) in the exhaust gas. The three-way catalyst has a function which is referred to as an oxygen storage function or an oxygen absorb function. The oxygen storage function is a function (1) to reduce nitrogen oxide in the exhaust gas by depriving oxygen from the nitrogen oxide when an air-fuel ratio of an air-fuel mixture is lean, so as to store the deprived oxygen inside, and (2) to release the stored oxygen to oxide unburnt substance in the exhaust gas when the air-fuel ratio of the air-fuel mixture is rich.
The above described oxygen storage function which relates to an exhaust gas purifying ability of the three-way catalyst can be maintained at a high level by activating a catalytic material (precious metal) owing to a repetition of the storage and the release of oxygen. In view of the above, an apparatus is widely known, which carries out a control (perturbation control) to forcibly fluctuate the air-fuel ratio of the exhaust gas (i.e., the air-fuel ratio of the air-fuel mixture) in order to cause the repetition of the storage and the release of oxygen in the three-way catalyst (refer to, for example, Japanese Patent Application Laid-Open (kokai Nos. Hei 2-11841, Hei 8-189399, Hei 10-131790, 2001-152913, 2005-76496, 2007-239698, 2007-56755, 2009-2170).